Another important quantity which measure the total correlation between two subsystems \(A\)  and \(B\)  in a mixed state is entanglement of purification (EoP) [1]}, [2]}. In general, we can purify a mixed state \(\rho _{AB}\)  to a pure state \(\vert \psi _{AA^{\prime }BB^{\prime }}\rangle \)  by enlarging the Hilbert space. The EoP is defined by the minimum of the EE between two subsystems \(AA^{\prime }\)  and \(BB^{\prime }\)  among all possible purifications. From this definition it is clear that the EoP between two subsystems \(A\)  and \(B\)  reduces to the EE of subsystem \(A\)  if one considers the subsystem \(B\)  as
complementary of subsystem \(A\) . There is a holographic prescription to calculate the EoP in which this quantity is dual to the minimal cross-section of entanglement wedge \(Ew\)  of \(\rho _{AB}\)  [3]}, [4]}. When \(\rho _{AB}\)  describes a pure state, \(Ew\)  between subsystems \(A\)  and \(B\)  reduces to the holographic entanglement entropy (HEE) of subsystem \(A\) . There are other correlation measures such as reflected
entropy, odd entropy and logarithmic negativity which are discussed in the literature and holographically all of them related to \(Ew\)  [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Various aspects of the EoP are discussed in the literature [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}.
